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Angles and Triangles Worksheet for Maths Olympiad

Maths Olympiad topic 21: Angles and triangles · Set 537 · 40 questions
TalentJR

How to solve it (180 is the magic number): The three angles of a triangle add up to 180°. An exterior angle equals the sum of the two interior angles opposite it. An isosceles triangle has two equal angles, opposite its two equal sides. Angles on a straight line add up to 180°; vertically opposite angles are equal.

NameDateTime takenScore ___ / 40
  1. 1.Two angles of a triangle are 60° and 65°. What is the third angle? (a) 125° (b) 55° (c) 115° (d) 120°
  2. 2.Two angles of a triangle are 35° and 75°. What is the third angle? (a) 70° (b) 145° (c) 110° (d) 105°
  3. 3.Two straight lines cross. Two vertically opposite angles add up to 310°. What is each of the other two angles? (a) 26° (b) 155° (c) 50° (d) 25°
  4. 4.Two straight lines cross. Two vertically opposite angles add up to 40°. What is each of the other two angles? (a) 160° (b) 140° (c) 20° (d) 320°
  5. 5.Two angles of a triangle are 35° and 65°. What is the exterior angle at the third corner? (a) 115° (b) 145° (c) 100° (d) 80°
  6. 6.Two angles of a triangle are 45° and 60°. What is the exterior angle at the third corner? (a) 135° (b) 105° (c) 75° (d) 120°
  7. 7.Two straight lines cross. One of the angles is 95°. What is the angle next to it on the same straight line? (a) 86° (b) 95° (c) 265° (d) 85°
  8. 8.In an isosceles triangle, the angle between the two equal sides is 70°. What is each of the other two angles? (a) 70° (b) 110° (c) 20° (d) 55°
  9. 9.Two angles of a triangle are 35° and 40°. What is the third angle? (a) 105° (b) 75° (c) 140° (d) 145°
  10. 10.Two straight lines cross. One of the angles is 85°. What is the angle next to it on the same straight line? (a) 275° (b) 5° (c) 95° (d) 85°
  11. 11.In an isosceles triangle, the angle between the two equal sides is 130°. What is each of the other two angles? (a) 50° (b) 25° (c) 130° (d) 35°
  12. 12.In an isosceles triangle, the two equal angles are 85° each. What is the third angle? (a) 85° (b) 10° (c) 5° (d) 95°
  13. 13.In an isosceles triangle, the two equal angles are 65° each. What is the third angle? (a) 65° (b) 25° (c) 50° (d) 115°
  14. 14.Two angles of a triangle are 40° and 70°. What is the exterior angle at the third corner? (a) 110° (b) 140° (c) 70° (d) 250°
  15. 15.Two angles of a triangle are 80° and 80°. What is the third angle? (a) 20° (b) 100° (c) 200° (d) 160°
  16. 16.Two angles of a triangle are 65° and 65°. What is the third angle? (a) 115° (b) 50° (c) 230° (d) 130°
  17. 17.Two straight lines cross. Two vertically opposite angles add up to 220°. What is each of the other two angles? (a) 71° (b) 70° (c) 110° (d) 140°
  18. 18.Two angles of a triangle are 25° and 25°. What is the third angle? (a) 310° (b) 130° (c) 155° (d) 50°
  19. 19.Two angles of a triangle are 75° and 45°. What is the third angle? (a) 105° (b) 135° (c) 120° (d) 60°
  20. 20.Two angles of a triangle are 35° and 70°. What is the exterior angle at the third corner? (a) 145° (b) 105° (c) 110° (d) 75°
  21. 21.Two straight lines cross. One of the angles is 160°. What is the angle next to it on the same straight line? (a) 200° (b) 20° (c) 160° (d) 21°
  22. 22.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 155° (b) 65° (c) 25° (d) 130°
  23. 23.In an isosceles triangle, the angle between the two equal sides is 20°. What is each of the other two angles? (a) 160° (b) 20° (c) 80° (d) 70°
  24. 24.Two angles of a triangle are 80° and 20°. What is the exterior angle at the third corner? (a) 80° (b) 160° (c) 100° (d) 260°
  25. 25.Two angles of a triangle are 60° and 30°. What is the third angle? (a) 90° (b) 150° (c) 120° (d) 270°
  26. 26.Two angles of a triangle are 65° and 80°. What is the exterior angle at the third corner? (a) 35° (b) 100° (c) 145° (d) 115°
  27. 27.Two angles of a triangle are 50° and 60°. What is the third angle? (a) 120° (b) 130° (c) 110° (d) 70°
  28. 28.Two angles of a triangle are 25° and 45°. What is the third angle? (a) 155° (b) 70° (c) 110° (d) 135°
  29. 29.Two angles of a triangle are 80° and 50°. What is the exterior angle at the third corner? (a) 130° (b) 50° (c) 100° (d) 230°
  30. 30.Two angles of a triangle are 60° and 80°. What is the exterior angle at the third corner? (a) 40° (b) 140° (c) 100° (d) 120°
  31. 31.Two angles of a triangle are 30° and 135°. What is the third angle? (a) 45° (b) 150° (c) 165° (d) 15°
  32. 32.Two angles of a triangle are 50° and 35°. What is the exterior angle at the third corner? (a) 145° (b) 85° (c) 130° (d) 95°
  33. 33.Two angles of a triangle are 35° and 55°. What is the exterior angle at the third corner? (a) 125° (b) 90° (c) 270° (d) 145°
  34. 34.Two angles of a triangle are 25° and 125°. What is the exterior angle at the third corner? (a) 150° (b) 55° (c) 30° (d) 155°
  35. 35.Two angles of a triangle are 65° and 100°. What is the third angle? (a) 15° (b) 165° (c) 115° (d) 80°
  36. 36.Two angles of a triangle are 30° and 65°. What is the third angle? (a) 85° (b) 150° (c) 95° (d) 115°
  37. 37.Two angles of a triangle are 80° and 60°. What is the third angle? (a) 120° (b) 100° (c) 140° (d) 40°
  38. 38.Two angles of a triangle are 55° and 20°. What is the exterior angle at the third corner? (a) 160° (b) 75° (c) 105° (d) 125°
  39. 39.Two angles of a triangle are 60° and 50°. What is the third angle? (a) 130° (b) 120° (c) 70° (d) 110°
  40. 40.Two angles of a triangle are 50° and 40°. What is the third angle? (a) 90° (b) 270° (c) 140° (d) 130°

Answer key

  1. 55°
  2. 70°
  3. 25°
  4. 160°
  5. 100°
  6. 105°
  7. 85°
  8. 55°
  9. 105°
  10. 95°
  11. 25°
  12. 10°
  13. 50°
  14. 110°
  15. 20°
  16. 50°
  17. 70°
  18. 130°
  19. 60°
  20. 105°
  21. 20°
  22. 130°
  23. 80°
  24. 100°
  25. 90°
  26. 145°
  27. 70°
  28. 110°
  29. 130°
  30. 140°
  31. 15°
  32. 85°
  33. 90°
  34. 150°
  35. 15°
  36. 85°
  37. 40°
  38. 75°
  39. 70°
  40. 90°

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